This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A381183 #24 Feb 23 2025 09:32:00 %S A381183 2,1,6,31,128,64,516,331,814,1607,4107,10158,10258,5129,10283,12819, %T A381183 25633,28141,16163,51404,80134,80864,40633,80216,40108,128129,250627, %U A381183 160626,80313,125641,208141,383814,391628,195814,156766,196314,391563,490641,806166,785313,628222,314111,625322,312661,1563305,2630104,1315052,657526,328763,1643815 %N A381183 a(n) = the smallest positive integer that produces a product that contains the digit 2 when multiplied by 2 at most n times, and where a further multiplication by 2 produces a number that does not contain the digit 2. Set a(n) = -1 if no such number exists. %C A381183 It is plausible that there are many terms, likely almost all terms, such that a(n) = -1, since the products as n increases become so large it is almost certain that subsequent products also contain the digit 2. It is therefore extremely unlikely that the series of products will terminate for very large values of n. See A381087. %C A381183 For all starting values up to 10^9 the lowest undetermined term is a(263), while the largest determined term is a(370) = 357131067. The largest term value in this range is a(301) = 957107659. %H A381183 Scott R. Shannon, <a href="/A381183/b381183.txt">Table of n, a(n) for n = 0..262</a> %e A381183 a(2) = 6 as 6*2 = 12, 12*2 = 24, 24*2 = 48, and the first two products contain the digit 2 while the third does not. %e A381183 a(6) = 516 as 516*2 = 1032, 1032*2 = 2064, 2064*2 = 4128, 4128*2 = 8256, 8256*2 = 16512, 16512*2 = 33024, 33024*2 = 66048, and the first six products contain the digit 2 while the seventh does not. %Y A381183 Cf. A381087, A378138, A011532. %K A381183 nonn,base %O A381183 0,1 %A A381183 _Michael De Vlieger_ and _Scott R. Shannon_, Feb 16 2025